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See the recommended documentation of this function
odedc
discrete/continuous ode solver
Calling Sequence
yt=odedc(y0,nd,stdel,t0,t,f)
Arguments
- y0
real column vector (initial conditions),
y0=[y0c;y0d]
wherey0d
hasnd
components.- nd
integer, dimension of
y0d
- stdel
real vector with one or two entries,
stdel=[h, delta]
(withdelta=0
as default value).- t0
real scalar (initial time).
- t
real (row) vector, instants where
yt
is calculated .- f
external i.e. function or character string or list with calling sequence:
yp=f(t,yc,yd,flag)
.
Description
y=odedc([y0c;y0d],nd,[h,delta],t0,t,f)
computes
the solution of a mixed discrete/continuous system. The discrete system
state yd_k
is embedded into a piecewise constant
yd(t)
time function as follows:
yd(t) = yd_k for t in [t_k=delay+k*h,t_(k+1)=delay+(k+1)*h[ (with delay=h*delta).
The simulated equations are now:
dyc/dt = f(t,yc(t),yd(t),0), for t in [t_k,t_(k+1)[ yc(t0) = y0c
and at instants t_k
the discrete variable
yd
is updated by:
yd(t_k+) = f(yc(t_k-),yd(t_k-),1)
Note that, using the definition of yd(t)
the last
equation gives
yd_k = f (t_k,yc(t_k-),yd(t_(k-1)),1) (yc is time-continuous: yc(t_k-)=yc(tk))
The calling parameters of f
are fixed:
ycd=f(t,yc,yd,flag)
; this function must return either
the derivative of the vector yc
if
flag=0
or the update of yd
if
flag=1
.
ycd=dot(yc)
must be a vector with same dimension
as yc
if flag=0
and
ycd=update(yd)
must be a vector with same dimension as
yd
if flag=1
.
t
is a vector of instants where the solution
y
is computed.
y
is the vector
y=[y(t(1)),y(t(2)),...]
. This function can be called
with the same optional parameters as the ode
function
(provided nd
and stdel
are given in
the calling sequence as second and third parameters). In particular
integration flags, tolerances can be set. Optional parameters can be set
by the odeoptions
function.
An example for calling an external routine is given in directory
SCIDIR/default/fydot2.f
External routines can be dynamically linked (see
link
).
Examples
//Linear system with switching input deff('xdu=phis(t,x,u,flag)','if flag==0 then xdu=A*x+B*u; else xdu=1-u;end'); x0=[1;1];A=[-1,2;-2,-1];B=[1;2];u=0;nu=1;stdel=[1,0];u0=0;t=0:0.05:10; xu=odedc([x0;u0],nu,stdel,0,t,phis);x=xu(1:2,:);u=xu(3,:); nx=2; plot2d1('onn',t',x',[1:nx],'161'); plot2d2('onn',t',u',[nx+1:nx+nu],'000'); //Fortran external( see fydot2.f): norm(xu-odedc([x0;u0],nu,stdel,0,t,'phis'),1) //Sampled feedback // // | xcdot=fc(t,xc,u) // (system) | // | y=hc(t,xc) // // // | xd+=fd(xd,y) // (feedback) | // | u=hd(t,xd) // deff('xcd=f(t,xc,xd,iflag)',... ['if iflag==0 then ' ' xcd=fc(t,xc,e(t)-hd(t,xd));' 'else ' ' xcd=fd(xd,hc(t,xc));' 'end']); A=[-10,2,3;4,-10,6;7,8,-10];B=[1;1;1];C=[1,1,1]; Ad=[1/2,1;0,1/20];Bd=[1;1];Cd=[1,1]; deff('st=e(t)','st=sin(3*t)') deff('xdot=fc(t,x,u)','xdot=A*x+B*u') deff('y=hc(t,x)','y=C*x') deff('xp=fd(x,y)','xp=Ad*x + Bd*y') deff('u=hd(t,x)','u=Cd*x') h=0.1;t0=0;t=0:0.1:2; x0c=[0;0;0];x0d=[0;0];nd=2; xcd=odedc([x0c;x0d],nd,h,t0,t,f); norm(xcd-odedc([x0c;x0d],nd,h,t0,t,'fcd1')) // Fast calculation (see fydot2.f) plot2d([t',t',t'],xcd(1:3,:)'); xset("window",2);plot2d2("gnn",[t',t'],xcd(4:5,:)'); xset("window",0);
See Also
<< ode_root | Differential Equations, Integration | odeoptions >> |